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Question Number 120706 by ZiYangLee last updated on 02/Nov/20

$$\mathrm{If}f\left(x\right)=x^4+{ax}^3+{bx}^2+cx+d$$$$f\left(1\right)=5,f\left(2\right)=10,f\left(3\right)=15$$$$\mathrm{find}f\left(9\right)+f(-5).$$

Commented by liberty last updated on 02/Nov/20

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}(\mathrm{x}-1)(\mathrm{x}-2)(\mathrm{x}-3)+5\mathrm{x}$$$$\to \{\begin{array}{l}\mathrm{f}\left(9\right)=9.8.7.6+45=3,069\\ \mathrm{f}(-5)=(-5)(-6)(-7)(-8)-25=1,655\end{array}$$$$\mathrm{f}\left(9\right)+\mathrm{f}(-5)=3,069+1,655=4,724$$$$$$

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